I think it'll take quite a few years for the spirit of democracy to really permeate our daily lives.
Literal
Democracy's spirit [subject-が] our daily-life's inside [into-に] permeate for [purpose-には], considerable years [subject-が] take [quotative-と] think.
The ~には following a verb is the purpose or condition sense — 'in order to X,' 'for X to happen.' It's a compact way to set up a condition and then make a claim about what that condition requires. Note how が marks the subject inside the subordinate clause (精神が浸透する) because は is already taken by the main-clause topic — a classic subordinate-vs-main clause particle split.